Problem: The symbols $\clubsuit$, $\bigstar$, $\blacklozenge$, and $\spadesuit$ each represent a distinct digit that has not been used already in the subtraction problem below. Whenever a symbol appears more than once, it represents the same digit each time. What is the digit that $\clubsuit$ represents in the following subtraction problem? \begin{tabular}{ r c c l} & 6& $\bigstar$ & $\blacklozenge$ \\ $-$ & $\clubsuit$ & 8 & $\blacklozenge$ \\ \hline &1 & $\spadesuit$ & $\bigstar$\\ \end{tabular}
From the units digit column, we deduce that $\bigstar=0.$ It follows that $\clubsuit$ must equal $\boxed{4}$. Alternately, we can note that $6-\clubsuit = 1,$ so $\clubsuit$ must equal either $4$ or $5.$ For the sake of contradiction, we assume that $\clubsuit = 5.$ It follows that $\bigstar \ge 7$ (including the possibility of carrying a digit from $\blacklozenge + \blacklozenge$) or else $\bigstar -8 <0.$ Additionally, $\bigstar$ must be even, since $\bigstar = 2 \blacklozenge.$ Thus, $\bigstar = 8.$ However, $\bigstar$ cannot equal $8$ because that digit is already taken. Contradiction. Hence, $\clubsuit=4,$ though we should check to ensure that this case actually works. Recall that $\bigstar$ is even, and cannot be $2,$ $4,$ $6,$ or $8,$ since that results in a reusing of digits. Hence, $\bigstar = 0,$ $\spadesuit = 2,$ and $\blacklozenge = 5,$ and $\clubsuit$ indeed equals $\boxed{4}.$